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# Re: st: RE: Question regarding meta-analysis for proportions.

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Question regarding meta-analysis for proportions. Date Sat, 30 Jul 2011 12:01:17 -0400

```Nora Trabulsi <nora.trabulsi@mail.mcgill.ca>:
I said log odds, not OR.
The log odds for a proportion p is logit(p) in Stata, and is undefined
for zero and one.
Why prefer log odds? Quoting from
http://www.stata-journal.com/sjpdf.html?articlenum=gr0010
"MacKay (2003, 316) asserts that, if we transform beta distributions
of variables P
between 0 and 1 to the corresponding densities over logit P = ln[P/(1
- P)], then
we find always pleasant bell-shaped densities. In contrast, densities
over P may have
singularities at P = 0 and P = 1."
This (in part) is why log odds, and differences in them, are used as a
measure of "effect size" for proportions.

On the relevance of the Beta distribution, see e.g.

On Sat, Jul 30, 2011 at 11:28 AM, Nora Trabulsi
<nora.trabulsi@mail.mcgill.ca> wrote:
> Thanks Austin
> The problem in my case is that I cannot use OR as there are no "unexposed" group. It is a meta analysis of phase 2 trials, in which all patients receive the intervention of interest and then the response(yes/no) rates are calculated, and that's why I thought of choosing proportions as the effect estimate.
>
> I have no experience with bayesian analysis in stata, however your approach sounds interesting and challenging! I must read about Bayesian in stata and give it a try and let you know.
>
> Thanks again
>
> Nora
>
> Sent from my iPhone
>
> On 2011-07-30, at 9:34 AM, "Austin Nichols" <austinnichols@gmail.com> wrote:
>
>> Nora Trabulsi <nora.trabulsi@mail.mcgill.ca> :
>> If you are working on a log odds scale as you should for meta-analysis
>> of proportions, you will have problems with the point estimate, not
>> just the standard error.  One way forward would be to use the mean and
>> variance of the posterior distribution in a Bayesian framework, with a
>> uniform prior in each study.  Probably true Bayesians would object to
>> this miscegenation of Bayesian and frequentist approaches, but I am
>> betting that if you simulate the approach, it dominates others in
>> terms of MSE.  It does not seem justifiable to remove the 2 studies
>> with the highest outcome from the analysis since you will introduce
>> bias by selecting on the outcome.
>>
>> On Thu, Jul 28, 2011 at 3:48 PM, Nora Trabulsi
>> <nora.trabulsi@mail.mcgill.ca> wrote:
>>>
>>> Yes, this is with using binomial exact. When I generated the proportions and their standard errors, the results shown in the the stata window shows "binomial exact".
<snip>>>>
>>>> I am doing a meta analysis on proportions of patients responding to specific treatment. I generated p(proportions) and  se(standard errors). Then , I used the metan command:
>>>>
>>>> metan p se, random
>>>>
>>>> The problem that I have encountered is that two of the studies that are included in the analysis had a response rate of 100%, however, they were small in size, 4 and 5 patients only. So this generated a problem as they had standard errors = zero and they were excluded form the analysis and forest plot.
>>>>
>>>> I tried to use the inverse weight command before running metan:
>>>>
>>>> gen cons=1
>>>> vwls p cons, sd(se)
>>>>
>>>> but it would still address the same problem, that std error theta cannot be negative or zero.
>>>>
>>>> Any idea how to solve this problem, or is it justifiable to remove those 2 studies from the analysis?

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